ALOM, MD. ASRAFUL and RASHID, MOHAMMED HARUNOR
(2017)
*GENERAL GAUSS-TYPE PROXIMAL POINT METHOD AND ITS CONVERGENCE ANALYSIS FOR SMOOTH GENERALIZED EQUATIONS.*
Asian Journal of Mathematics and Computer Research, 15 (4).
pp. 296-310.

## Abstract

Let X and Y be Banach spaces and Ω be an open subset of X. In the present paper, a general Gauss-type Proximal Point Algorithm (GGPPA) is introduced for approximating the solution of a generalized equation 0∈f(x)+F(x), where f:X→ Y is a differentiable function on Ω and F:X⇉2^Y is a set valued mapping with closed graph. Semilocal and local convergences of the GGPPA are presented by considering a sequence of Lipschitz continuous functions gk:X→ Y such that gk (0)=0 around the origin with positive Lipschitz constants λk and the metric regularity condition of F. Finally, we give a numerical example to verify the convergence results of the GGPPA.

Item Type: | Article |
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Subjects: | Article Paper Librarian > Mathematical Science |

Depositing User: | Unnamed user with email support@article.paperlibrarian.com |

Date Deposited: | 27 Dec 2023 07:08 |

Last Modified: | 27 Dec 2023 07:08 |

URI: | http://editor.journal7sub.com/id/eprint/2463 |